The concentration of alcohol in a person’s bloodstream is measurable. Suppose that the relative risk R of having an accident while driving a car can be modeled by an equation of the formR = ekx where x is the percent concentration of alcohol in the bloodstream and k is a constant. (a) Suppose that a concentration of alcohol in the bloodstream of 0.03 percent results in a relative risk of an accident of 1.4. Find the constant k in the equation.(b) Using this value of k, what is the relative risk if the concentration is 0.17 percent?(c) Using the same value of k, what concentration of alcohol corresponds to a relative risk of 100?(d) If the law asserts that anyone with a relative risk of having an accident of 5 or more should not have driving privileges, at what concentration of alcohol in the bloodstream should a driver be arrested and chargedwith a DUI?(e) Compare this situation with that of Example 10. If you were a lawmaker, which situation would you support?Give your reasons.
The concentration of alcohol in a person’s bloodstream is measurable. Suppose that the relative risk R of having an accident while driving a car can be modeled by an equation of the form
R = ekx
where x is the percent concentration of alcohol in the bloodstream and k is a constant.
(a) Suppose that a concentration of alcohol in the bloodstream of 0.03 percent results in a relative risk of an accident of 1.4. Find the constant k in the equation.
(b) Using this value of k, what is the relative risk if the concentration is 0.17 percent?
(c) Using the same value of k, what concentration of alcohol corresponds to a relative risk of 100?
(d) If the law asserts that anyone with a relative risk of having an accident of 5 or more should not have driving privileges, at what concentration of alcohol in the bloodstream should a driver be arrested and charged
with a DUI?
(e) Compare this situation with that of Example 10. If you were a lawmaker, which situation would you support?
Give your reasons.
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